He differs from Rabbi Hiyya; for Rabbi Hiyya said: He places them on his table {so he can go into the meal room with Tefilin and putting them on table}, and so it is becoming for him {to be available to take them for time of blessing (graces) }. How long does he leave them there? Until the time for grace.

He may eat only a snack while wearing them. If, however, he enters to partake of a regular meal, he should remove them and place them on the table until after he washes his hands [at the conclusion of the meal]. Afterwards, he should put them on and recite grace over his meal while wearing them.

Conclusion: That is perfectly allowed to drink a Coffee wearing tefilin.

Seudat Keva is forbidden, but Arai is allowed.
Coffee is usually drunk as a Keva meal, a permanent meal, so in that case i think it would be forbidden, but then again if it is a part of some kiddush after Tefillah, and one is still wearing his Tefillin, in my opinion it's considered Arai, and is allowed. והשם יראה ללבב.

Consequently, light drinks, such as water or soda, are allowed anyways.

Hi Avichai. We don't know you that we should trust you, so without source citations, this answer isn't that useful to the community. Please edit in source references to support your claims.
– Double AA♦May 25 '16 at 13:35